Using the Pythagorean theorem, the distance between two points (x1, y1) and (x2, y2) is gotten as follows:
![\begin{gathered} d^2=(x_2-x_1)^2+(y_2-y_1)^2 \\ \text{Thus:} \\ d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/i5lwnzod7gftwml84zon9mzcutkpfaiig1.png)
Since we have the two coordinates: (2, 8) and (-8, 2)
where:
(x1, y1)= (2, 8)
(x2, y2) = (-8, 2)
Therefore, the distance between them is:
![\begin{gathered} d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ d=\sqrt[]{((-8)_{}-2_{})^2+(2-8)^2} \\ d=\sqrt[]{((-10_{})^2+(-6)^2} \\ d=\sqrt[]{100+36} \\ d=\sqrt[]{136} \\ d=11.66 \\ d=11.7\text{ (to one decimal place)} \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/e8jtzwto6y5efssqci3g7p0z1y62lbxae2.png)
Therefore, the distance between the two p is: 11.7
Correct option is: Option D